Rewrite as a simplified fraction. ${2.\overline{51} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 251.5151...\\ 1x &= 2.5151...\end{align*}}$ Subtracting the two equations, we have: ${99x = 249}$ ${x = \dfrac{249}{99}} $ ${x = \dfrac{83}{33}} \text{or} {2 \dfrac{17}{33}}$